A337563 Number of pairwise coprime unordered triples of positive integers > 1 summing to n.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 1, 4, 0, 7, 1, 7, 3, 9, 2, 15, 3, 13, 5, 17, 4, 29, 5, 20, 8, 28, 8, 42, 8, 31, 14, 42, 10, 59, 12, 45, 21, 52, 14, 77, 17, 68, 26, 69, 19, 101, 26, 84, 34, 86, 25, 138, 28, 95, 43, 111, 36, 161, 35, 118, 52, 151

Offset: 0

Author

Gus Wiseman, Sep 21 2020

Keywords

• nonn

Comments

Such partitions are necessarily strict.

The Heinz numbers of these partitions are the intersection of A005408 (no 1's), A014612 (triples), and A302696 (coprime).

Examples

			The a(10) = 1 through a(24) = 15 triples (empty columns indicated by dots, A..J = 10..19):
  532  .  543  .  743  753  754  .  765  B53  875  975  985  B75  987
          732     752       853     873       974  B73  B65  D73  B76
                            952     954       A73  D53  B74       B85
                            B32     972       B54       B83       B94
                                    B43       B72       B92       BA3
                                    B52       D43       D54       C75
                                    D32       D52       D72       D65
                                                        E53       D74
                                                        H32       D83
                                                                  D92
                                                                  F72
                                                                  G53
                                                                  H43
                                                                  H52
                                                                  J32
		

Links

• Fausto A. C. Cariboni, Table of n, a(n) for n = 0..10000

Crossrefs

A055684 is the version for pairs.

A220377 allows 1's, with non-strict version A307719.

A337485 counts these partitions of any length.

A337563*6 is the ordered version.

A001399(n - 3) = A069905(n) = A211540(n + 2) counts 3-part partitions.

A002865 counts partitions with no 1's, with strict case A025147.

A007359 counts pairwise coprime partitions with no 1's.

A078374 counts relatively prime strict partitions.

A200976 and A328673 count pairwise non-coprime partitions.

A302696 ranks pairwise coprime partitions.

A302698 counts relatively prime partitions with no 1's.

A305713 counts pairwise coprime strict partitions.

A327516 counts pairwise coprime partitions.

A337452 counts relatively prime strict partitions with no 1's.

Cf. A007304, A082024, A101268, A284825, A332004, A337451, A337461, A337462, A337561, A337599, A337601, A337605.

Programs

Mathematica

Table[Length[Select[IntegerPartitions[n,{3}],!MemberQ[#,1]&&CoprimeQ@@#&]],{n,0,30}]